A359064 - OEIS

A359064

a(n) is the number of trees of order n such that the number of eigenvalues of the Laplacian matrix in the interval [0, 1) is equal to ceiling((d + 1)/3) = A008620(d), where d is the diameter of the tree.

%I #6 Dec 15 2022 13:39:06

%S 2,5,7,12,20,33,52,86,137,222,353,568,900,1433,2260,3574

%N a(n) is the number of trees of order n such that the number of eigenvalues of the Laplacian matrix in the interval [0, 1) is equal to ceiling((d + 1)/3) = A008620(d), where d is the diameter of the tree.

%H Jiaxin Guo, Jie Xue, and Ruifang Liu, <a href="https://arxiv.org/abs/2212.05283">Laplacian eigenvalue distribution, diameter and domination number of trees</a>, arXiv:2212.05283 [math.CO], 2022.

%F Conjecture from Guo et al.: lim_{n->oo} a(n)/A000055(n) = 0.

%Y Cf. A000055, A008620.

%K nonn,more

%O 5,1

%A _Stefano Spezia_, Dec 15 2022